V.H
Nov. 10, 2009
Math 7D Big Idea: Many important practical and mathematical applications involve comparing quantities of one kind or another; it is important to know which method to use and how we should use them.
Essential Question: What methods are there for comparing things? Vocabulary:
Percent: A fraction with the replaced ‘out of 100’ shown in this symbol: %.
Notes:
If you want to convert a part-to-part ratio to a percent, first you change the ratio to part to whole (by adding both parts for the fraction denominator, and taking the first part for the numerator), converting this to a decimal, and then to a percent.
1. Give an Example of a situation in which it makes sense to use percents to make comparisons.
Ms. Andrea wants to separate her students in 3 groups: beginners, intermediates, and advanced. She has 50 students in total. 6 students ar at the beginner level, 29 are in the intermediate, and 15 students are in advanced.
(Very easy to turn these fractions into percents)
2. Using your example from part 1, show how to make a comparison using percents.
58% of the students are in Ms. Andrea’s intermediate group and 42%are not.
3. Explain why percents are useful for making comparisons.
Percents are good for making comparisons because they show part to whole instead comparisons of part to part like in a ratio. Percents are easy to convert and help you understand a more complex fraction.
4. Give an example of a situation in which you think another form of comparison is better than percents. Explain your reasoning.
Luis tested 5 people for his science experiment. His experiment was testing whether people when asked a math question would change answers when a variable was added (but the other variables may not match what they’re told to be). 3 people did not change their answer, and 2 didn’t. Therefore, the ratio of who did and who didn’t is 3:5
Ratios are better to use here because you are dealing with small numbers without drastic differences. Percents would just enlarge the numbers.
5. Can you find a percent comparison from a ratio comparison? Explain how, or tell what additional information you would need.
You can find a percent comparison from a ratio comparison by making a fraction out of the ratio, changing it to a decimal, and then changing it to a percent.
Summary:
Percents are very simple ways of writing complex fractions. I have mostly mastered percents even before this sub-unit, and hope I will be able to use more ratios (which I have not ‘mastered’ yet) in the next unit. I may want to practice the skill of finding whole percents without using a calculator, and hopefully the next ACE problems will involve some percents that will allow me to use my mental math but still check my work on a calculator.
Nov. 10, 2009
Math 7D
Big Idea:
Many important practical and mathematical applications involve comparing quantities of one kind or another; it is important to know which method to use and how we should use them.
Essential Question: What methods are there for comparing things?
Vocabulary:
Percent: A fraction with the replaced ‘out of 100’ shown in this symbol: %.
Notes:
If you want to convert a part-to-part ratio to a percent, first you change the ratio to part to whole (by adding both parts for the fraction denominator, and taking the first part for the numerator), converting this to a decimal, and then to a percent.
1. Give an Example of a situation in which it makes sense to use percents to make comparisons.
Ms. Andrea wants to separate her students in 3 groups: beginners, intermediates, and advanced. She has 50 students in total. 6 students ar at the beginner level, 29 are in the intermediate, and 15 students are in advanced.
(Very easy to turn these fractions into percents)
2. Using your example from part 1, show how to make a comparison using percents.
58% of the students are in Ms. Andrea’s intermediate group and 42% are not.
3. Explain why percents are useful for making comparisons.
Percents are good for making comparisons because they show part to whole instead comparisons of part to part like in a ratio. Percents are easy to convert and help you understand a more complex fraction.
4. Give an example of a situation in which you think another form of comparison is better than percents. Explain your reasoning.
Luis tested 5 people for his science experiment. His experiment was testing whether people when asked a math question would change answers when a variable was added (but the other variables may not match what they’re told to be). 3 people did not change their answer, and 2 didn’t. Therefore, the ratio of who did and who didn’t is 3:5
Ratios are better to use here because you are dealing with small numbers without drastic differences. Percents would just enlarge the numbers.
5. Can you find a percent comparison from a ratio comparison? Explain how, or tell what additional information you would need.
You can find a percent comparison from a ratio comparison by making a fraction out of the ratio, changing it to a decimal, and then changing it to a percent.
Summary:
Percents are very simple ways of writing complex fractions. I have mostly mastered percents even before this sub-unit, and hope I will be able to use more ratios (which I have not ‘mastered’ yet) in the next unit.
I may want to practice the skill of finding whole percents without using a calculator, and hopefully the next ACE problems will involve some percents that will allow me to use my mental math but still check my work on a calculator.